Analysis of the Functioning and Structural Decomposing of Special-Purpose Information Systems

On the basis of the analysis of the functioning of complex special-purpose information systems, a general approach was proposed to their mathematical modeling and structural decomposition, based on topological constructions using the theory of the final semigroups. The connection between any transformations of a complex system in the finite space of its states and certain valid coordinatization variants is defined for the final semigroups. Various generalized indicators of evaluation of functional structure simplexes, which allowed one to obtain the characteristics of these complexes, have been determined. The proposed method of analysis allowed more objective analysis of the q-connectivity of the simplexes and the observability and controllability of the special-purpose complex information system. Definitions, theorems, and proofs are presented, which allows calculation of the sequence of composition and the integration of the subsystems of a complex system into a single whole.